STAT FINAL

Which of the following is not a characteristic of the t distribution? It is a continuous distribution. It has a mean of 0. It is a symmetric distribution. It approaches z as degrees of freedom decrease.

It approaches z as degrees of freedom decrease.

The Central Limit Theorem (CLT): applies only to samples from normal populations. applies to any population. applies best to populations that are skewed. applies only when μ and σ are known.

applies to any population.

A _________ is a range of numbers inferred from the sample that has a certain probability of including the population over the long run hypothesis lower limit confidence interval probability limit

confidence interval

A _________ is a subset of _________ sample, population population, sample statistic, parameter parameter, statistic

sample, population

A _________ is a numerical characteristic of a sample and a _________ is a numerical characteristic of a population sample, population population, sample statistic, parameter parameter, statistic

statistic, parameter

What does it mean when you calculate a 95% confidence interval? - The process you used will capture a true parameter 95% of the time in the long run - You can be "95% confident" that your interval will include the population parameter - You can be "5% confident" that your interval will not include the population parameter - All of the above

All of the above

As the sample size increases, the standard error of the mean:

Decreases

A 90 percent confidence interval will be wider than a 95 percent confidence interval, ceteris paribus.

F

In a sample size calculation, if the confidence level decreases, the size of the sample needed will increase.

F

The Central Limit Theorem says that, if n exceeds 30, the population will be normal.

F

Which of the following statements is most nearly correct, other things being equal? Using Student's t instead of z makes a confidence interval narrower. The table values of z and t are about the same when the mean is large. For a given confidence level, the z value is always smaller than the t value. Student's t is rarely used, because it is more conservative to use z.

For a given confidence level, the z value is always smaller than the t value.

Which of the following is not a characteristic of the t distribution? It is a continuous distribution It has a mean of 0 It a symmetric distribution It is similar to the z distribution when n is small

It is similar to the z distribution when n is small

What would happen (other things equal) to a confidence interval if you calculated a 99 percent confidence interval rather than a 95 percent confidence interval? It will be narrower It will not change The sample size will increase It will become wider

It will become wider

A 90 percent confidence interval will be narrower than a 95 percent confidence interval, ceteris paribus.

T

As n increases, the width of the confidence interval will decrease, ceteris paribus.

T

For a sample size of 20, a 95 percent confidence interval using the t distribution would be wider than one constructed using the z distribution.

T

In constructing a confidence interval for a mean, the width of the interval is dependent on the sample size, the confidence level, and the population standard deviation.

T

In constructing a confidence interval for the mean, the z distribution provides a result nearly identical to the t distribution when n is large.

T

The Student's t distribution is always symmetric and bell-shaped, but its tails lie above the normal.

T

When the sample standard deviation is used to construct a confidence interval for the mean, we would use the Student's t distribution instead of the normal distribution.

T

Concerning confidence intervals, which statement is most nearly correct? We should use z instead of t when n is large. We use the Student's t distribution when σ is unknown. We use the Student's t distribution to narrow the confidence interval.

We use the Student's t distribution when σ is unknown.

For a given sample size, the higher the confidence level, the: more accurate the point estimate. smaller the standard error. smaller the interval width. greater the interval width.

greater the interval width.

The Central Limit Theorem (CLT) implies that:

the distribution of the mean is approximately normal for large n.

The width of a confidence interval for μ is not affected by:

the sample mean

A sample size goes up, what tends to happen to 95% confidence intervals They become more precise they becomes more narrow they become wider Both a and b

they become more narrow